Question 1080804
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<pre>
The general equation of a straight line parallel to the given line is

x + 2y + c = 0,

where "c" is some constant.


If we want our straight line be parallel to the given line and pass at the distance of 2 from the origin (x,y) = (0,0), 
we must find "c" from this equation


{{{abs(c)/sqrt(1^2 + 2^2)}}} = 2    (1)


(see the lesson <A HREF=https://www.algebra.com/algebra/homework/Vectors/The-distance-from-a-point-to-a-straight-line-in-a-coordinate-plane.lesson>The distance from a point to a straight line in a coordinate plane</A> in this site).


From equation (1), |c| = {{{2*sqrt(5)}}},  so c can have two values: c = {{{2*sqrt(5)}}}  or  c = {{{-2*sqrt(5)}}}.


Thus, the two equations the problem asks for are

{{{x + 2y + 2*sqrt(5)}}} = 0   (2)

and

{{{x + 2y - 2*sqrt(5)}}} = 0   (3).
</pre>

Solved.



Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lesson is the part of this online textbook under the topic 
"<U>The distance from a point to a straight line in a coordinate plane</U>".